There are various stages of hypothermia to be aware of in terms of signs and sometimes improvement in a sign is an indication that the animal is getting worse, especially when talking about shivering. Early stages have shivering, it abates at later stages, so keeping an eye on your pet is critically important in this case.
Very young and very old animals are at greater risk as are smaller animals with less natural defence. For mild or moderate hypothermia, you can treat with active external warming such as warm blankets, warm moving air, and the like, though checking with a vet is advised for moderate hypothermia. For severe hypothermia, you must seek medical assistance from a vet, though starting the warming process by drying and covering them is important too.
Whatever you do, do not, however, put the dog into a warm water bath as it could kill them from the shock.
One thing you might want to do is find out how to take your dogs temperature, have your vet demonstrate it if possible. Knowing this will allow you to check, dogs should have a core body temperature around 101° - 102.5° so dropping below that indicates too cold (as a note, cats are similar and have the same warning signs).
Mild (95° - 99°)
- Lethargic
- Signs of weakness
- Shivering (dogs and cats seldom shiver, pay attention for this sign especially)
- Signs of confusion or agitation
- Variable rate of breathing
- Feels cold
Moderate (90° - 95°)
- Collapse
- Shivering abates
- Appears to have stiff muscles
- Shallow and slowed breathing
Severe (< 90°)
- No shivering
- Appears to have stiff muscles
- Dilated pupils
- Shallow and slowed breathing
- May have coughing with signs of blood (sign of fluids in the lungs)
Main Sources (for additional reading if you want)
- The First Aid Companion for Dogs & Cats, Amy D Shojai
- Blackwell's Five-Minute Veterinary Consult: Canine and Feline, 5th edition, Larry P. Tilley and Francis W.K. Smith, Jr.